Non-redundant, linear-phase, semi-orthogonal, directional complex wavelets [image/video processing applications]

The directionality and phase information provided by nonredundant complex wavelet transforms (NCWTs) provide significant potential benefits for image/video processing and compression applications. However, because existing NCWTs are created by downsampling filtered wavelet coefficients, the finest scale of these transforms has a resolution 4× lower than the real input signal. In this paper, we propose a linear-phase, semi-orthogonal, directional NCWT design using a novel triband filter bank. At the finest scale, the resulting transform has a resolution 3× lower than the real input signal. We provide a design example to demonstrate three important properties for image/video processing applications: directionality, magnitude coherency, and phase coherency.